Published October 1, 2012
| Version v1
Journal article
Higher secant varieties of $\mathbb P^n \times\mathbb P^ 1$ embedded in bi-degree $(a,b)$
Contributors
Others:
- University of Trento [Trento]
- Geometry, algebra, algorithms (GALAAD) ; Inria Sophia Antipolis - Méditerranée (CRISAM) ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
- Dipartimento di Ingegneria della produzione, termoenergetica e modelli matematici (DIPTEM) ; Università degli studi di Genova = University of Genoa (UniGe)
- European Project: 252367,EC:FP7:PEOPLE,FP7-PEOPLE-2009-IEF,DECONSTRUCT(2010)
Description
In this paper we compute the dimension of all the higher secant varieties to the Segre-Veronese embedding of $\mathbb{P}^n\times \mathbb{P}^1$ via the section of the sheaf $\mathcal{O}(a,b)$ for any $n,a,b\in \mathbb{Z}^+$. We relate this result to the Grassmann Defectivity of Veronese varieties and we classify all the Grassmann $(1,s-1)$-defective Veronese varieties.
Abstract
19 pagesAbstract
International audienceAdditional details
Identifiers
- URL
- https://hal.inria.fr/hal-00646167
- URN
- urn:oai:HAL:hal-00646167v1
Origin repository
- Origin repository
- UNICA